Selected Works, Volume 1: Selected Research Papers

✍ Scribed by L. S. Pontryagin, R. V. Gamkrelidze (editor)

• Publisher: CRC Press
• Year: 2019
• Tongue: English
• Leaves: 639
• Series: Classics of Soviet Mathematics
• Edition: Reprint
• Category: Library

✦ Synopsis

Among the finest achievements in modern mathematics are two of L.S. Pontryagin`s most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory. On 3 September 1983 Lev Semenovich Pontryagin was seventy-five. To mark this important event in the life of this outstanding contemporary mathematician we are beginning the publication of his scientific works in four volumes, according to a decision taken by the Mathematics Division of the USSR Academy of Sciences. The first volume contains the most important mathematical papers of L. S. Pontryagin and also includes a bibliography of his basic scientific works, the second is his well-known monograph Topological Groups, the third comprises two monographs, Foundations of Algebraic Topology and Smooth Manifolds and Their Applications in Homotopy Theory, and the fourth is a revised edition of The Mathematical Theory of Optimal Processes by L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko.

✦ Table of Contents

Preface, Zum Alexanderschen Dualitätssatz, Zum Alexanderschen Dualitätssatz Zweite Mitteilung, Sur une Hypothèse Fondamentale de la Théorie de la Dimension, Über den Algebraischen Inhalt Topologischer Dualitätssätze, Beweis des Mengerschen Einbettungssatzes, Über Stetige Algebraiche Körper, On Dynamical Systems Close to Hamiltonian Systems, The Theory of Topological Commutative Groups, The General Topological Theorem of Duality for Closed Sets, Sur les Groupes Topologiques Compacts et le Cinquième Problème de M. Hilbert, Sur les Nombres de Betti des Groupes de Lie, Rough Systems, The Classification of Continuous Mappings of a Complex into a Sphere. Communication I, The Classification of Continuous Mappings of a Complex into a Sphere. Communication II, Homologies in Compact Lie Groups, Über die Topologische Struktur der Lieschen Gruppen, A Classification of Mappings of the Three-Dimensional Complex into the Two-Dimensional Sphere, On the Zeros of Certain Elementary Transcendental Functions, Mappings of a Three-Dimensional Sphere into an «-Dimensional Complex, Characteristic Cycles of Manifolds, A Method of Calculation of Homology Groups, Hermitian Operators in a Space With an Indefinite Metric, The Classification of Certain Skew Products, Characteristic Cycles, Topological Duality Theorems, Characteristic Cycles of Differentiable Manifold, On Certain Topological Invariants of Closed Riemannian Manifolds, Homotopic Classification of the Mappings of an (n + 2)-Dimensional Sphere into an «-Dimensional Sphere, On the Zeros of Certain Elementary Transcendental Functions (Supplement), The Asymptotic Behaviour of the Solutions of Systems of Differential Equations With a Small Parameter Attached to Higher Derivatives, Optimal Control Processes, Linear Differential Games, Linear Differential Evasion Games, Linear Differential Pursuit Games